Problem: What is the digit in the thousandths place of the decimal equivalent of $\frac{3}{16}$?
Solution: Since the denominator of $\dfrac{3}{16}$ is $2^4$, we multiply numerator and denominator by $5^4$ to obtain  \[
\frac{3}{16} = \frac{3\cdot 5^4}{2^4\cdot 5^4} = \frac{3\cdot 625}{10^4} = \frac{1875}{10^4} = 0.1875.
\] The digit in the thousandths place is $\boxed{7}$.